Towards the capacity region of multiplicative linear operator broadcast channels

Recent research indicates that packet transmission employing random linear network coding can be regarded as transmitting subspaces over a linear operator channel (LOC). In this paper we propose the framework of linear operator broadcast channels (LOBCs) to model packet broadcasting over LOCs, and we do initial work on the capacity region of constant-dimension multiplicative LOBCs (CMLOBCs), a generalization of broadcast erasure channels. Two fundamental problems regarding CMLOBCs are addressed-finding necessary and sufficient conditions for degradation and deciding whether time sharing suffices to achieve the boundary of the capacity region in the degraded case.